Anatoly Shcharansky will be honored today in the Capitol Rotunda and will meet with President Reagan. And while his 10-day visit to the United States is meant to increase support for Soviet Jewish emigration and to thank some of those who helped free him last February after nine years in Russian jails, he is sometimes overwhelmed by his new role as hero and symbol.

"I saw him in Israel and he told me that in the Soviet Union he knew who his enemy was and that he had a clear sense of fighting that enemy," said Zeesy Schnur, the executive director of the Coalition to Free Soviet Jews. "Now he said he has to deal with an 'ocean of love,' and sometimes an ocean of love is as difficult to deal with as an ocean of hate."

Since Shcharansky walked across the Glienicke Bridge in Berlin to freedom three months ago and flew to Jerusalem, he has been besieged by groups who want to meet with him. His admirers leave gifts on his doorstep. Some come in the middle of the night.

Shcharansky and his wife Avital, who is pregnant and remained in Israel this week, finally taped a sign to their apartment door: "We very much appreciate your coming to see us, but . . . we cannot possibly receive you. Please show kindness and neither ring our bell nor knock on our door."

Dan Klores, who works for Howard Rubenstein Associates, the public relations firm handling Shcharansky's visit to the United States, said, "There have been literally thousands of requests to meet him. They've come from all 50 states, Jewish organizations in every corner of the country, veterans' groups, tiny radio stations from San Antonio, Cleveland, lots of synagogues and rabbis."

As Shcharansky told People magazine, "For now, I am trying to remain independent of all outside influences . . . The problem is that there are so many Jewish organizations, all wanting to pull me in different directions. Sometimes I have nightmares. Some of them are about the Soviet guards outside the punishment cell, but nowadays, I chuckle because some of them are about the heads of those Jewish organizations."

To avoid offending groups or individuals, Shcharansky arrived in New York Thursday without a particular host but with two full-time security guards.

"Shcharansky doesn't want to appear like he's favoring anybody," Klores said. "It's a tricky thing to manage. Monday morning he met with leaders of the Soviet Jewry campaign. But not just one group. He met with all the big ones."

Other prominent Soviet e'migre's have attracted much attention in the West, but few have had the magnetism of Shcharansky. Alexander Solzhenitsyn, for example, was a hero to many Americans, but a remote, distinctly Russian figure who has lived mainly in an isolated Vermont village, emerging occasionally to publish a book or criticize U.S. foreign policy.

Shcharansky, on the other hand, is a hero who emerged from hell smiling and joking. At a rally in New York Sunday attended by 300,000, he spoke with gratitude about the activists who have struggled to help him, and other thousands of other Soviet Jews, leave Russia. About 400,000 of the Soviet Union's 2.5 million Jews have applied to emigrate, but since 1980 the country has cut emigration to a trickle.

When Shcharansky first arrived in Israel, he adopted a Hebrew first name, Natan, and was carried aloft, like a bobbing cork, on the shoulders of his new countrymen.

In Washington the reception will be a bit less public, if equally jubilant. After meeting with Reagan and other officials, he will return to New York Friday. He returns to Israel on Tuesday.

"Natan came here wanting to touch everyone, speak to everyone," Schnur said. "Anyone else would have been completely exhausted with this schedule. But he can survive anything."